No Convergence (Negative Binomial Model)

[Sebastian Witteler]

I examine the number of co-publications by six countries that are member of a regional organization over the last 31 years. I'm particularly interested in similarities and differences of the countries' co-authorship patterns, especially in those variables that reflect the relation to co-authors' countries such as the trade volume or the geographical distance. For this purpose, I've decided to apply a population-averaged negative binomial model using -xtnbreg, pa difficult vce(robust)- following the field-specific literature's recommendation for the case of overdispersed data.

I'm currently, however, at an impasse because including any of these "pair variables" (or virtual proximity variables) results in -no convergence-.

Now this issue is certainly not new and I have found helpful explanations and advice in previous forum threads [1,2,3,4,5] - but I'm not sure if I understand all of it properly and I'm a bit uncertain about which of them apply to my specific case. I have summarized potential issues, their recommended remedies and what I've tried so far to give you a better overview on my current understanding. Please indicate if you see something that I got wrong.

1. It may be the case that there is high collinearity between independent variables [5]. Some year dummies at the end of the time period are dropped due to collinearity but checking correlations with -pwcorr- shows relatively weak correlations between pair variables (<0.4) while they are higher between those variables that reflect the domestic dimension (where convergence is achieved). -no convergence- is also an issue if I exclude the year dummies so I don't think this should be an issue.

2. There is the possibility that the maximum likelihood estimator for my model "does not exist" for my data [1]. This seems to be a possible option as my data has indeed a large number of 0 values in the dependent variable and the "pair" independent variables. A potential remedy would be to start with a poisson regression and plugin the estimates into the negative binomial regression [2]. I wasn't sure what model I should use so I've just run a population-averaged poisson regression -xtpoisson, pa- but it results in -no convergence- as well. I assume using these estimates probably won't help neither, right?

3. In case of using an interaction, the model including the interaction may not be identified by the data [4]. I'm not using interactions so that specific issue should not apply here.

4. My model is insufficient and I should try something different.

I've tried to use -difficult- option to change the steps during the iteration [4], however, to no avail. I have tried to use -xtpoisson, r fe- as a fall back option [3] but with the same result. What I haven't thoroughly tried so far is to use another maximization technique as I lack proper understanding of the particularities of the different techniques.

I should mention that I have isues with an empty Wald chi² statistic that I attribute to a scaling problem as I was able to fix it by re-scaling the problematic pair variables.

Do you have some recommendations on possible next steps?

I've attached an example of the regression and copied the output below for a better overview.

. xtset target year
       panel variable:  target (strongly balanced)
        time variable:  year, 1988 to 2018
                delta:  1 unit

xtnbreg collab_weight rtot_trade gdp_pc tertenrol_epol trade_percgdp mobcell100 colotrad langcom i.year, pa difficult vce(robust)
note: 2015.year omitted because of collinearity
note: 2016.year omitted because of collinearity
note: 2017.year omitted because of collinearity
note: 2018.year omitted because of collinearity

Iteration 1: tolerance = .31055186
Iteration 2: tolerance = .07928357
Iteration 3: tolerance = .08383659
Iteration 4: tolerance = .04340788
Iteration 5: tolerance = .22333106
.
.
.
Iteration 95: tolerance = .23854644
Iteration 96: tolerance = .19215449
Iteration 97: tolerance = .23957639
Iteration 98: tolerance = .20948912
Iteration 99: tolerance = .26024878
Iteration 100: tolerance = .10269846

GEE population-averaged model                   Number of obs     =      3,161
Group variable:                     target      Number of groups  =        109
Link:                                  log      Obs per group:
Family:             negative binomial(k=1)                    min =         29
Correlation:                  exchangeable                    avg =       29.0
                                                              max =         29
                                                Wald chi2(31)     =   10794.89
Scale parameter:                         1      Prob > chi2       =     0.0000

                                   (Std. Err. adjusted for clustering on target)
--------------------------------------------------------------------------------
               |             Semirobust
 collab_weight |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
    rtot_trade |   2.60e-09   6.37e-09     0.41   0.683    -9.88e-09    1.51e-08
        gdp_pc |   .0000971   .0000247     3.94   0.000     .0000487    .0001454
tertenrol_epol |   2.22e-06   4.01e-07     5.53   0.000     1.43e-06    3.01e-06
 trade_percgdp |  -.0183561   .0116593    -1.57   0.115    -.0412079    .0044958
    mobcell100 |   .0073132   .0011522     6.35   0.000     .0050549    .0095715
      colotrad |   1.594459   .5851681     2.72   0.006     .4475504    2.741367
       langcom |   1.509419   .6002954     2.51   0.012     .3328614    2.685976
               |
          year |
         1991  |   .2856466   .3194495     0.89   0.371    -.3404629    .9117561
         1992  |  -.0231025   .2237049    -0.10   0.918     -.461556     .415351
         1993  |   .4922213   .1874601     2.63   0.009     .1248063    .8596362
         1994  |   .4741249   .2524005     1.88   0.060     -.020571    .9688208
         1995  |   .4691006   .2529398     1.85   0.064    -.0266523    .9648535
         1996  |   .4894541   .1945354     2.52   0.012     .1081717    .8707365
         1997  |    .927893   .2780302     3.34   0.001     .3829638    1.472822
         1998  |   1.250811   .2103598     5.95   0.000     .8385137    1.663109
         1999  |   1.082485   .2243396     4.83   0.000     .6427869    1.522182
         2000  |     .96179   .2667751     3.61   0.000     .4389204     1.48466
         2001  |   .9312558   .1905119     4.89   0.000     .5578593    1.304652
         2002  |   .8492289   .1903188     4.46   0.000     .4762109    1.222247
         2003  |   .9112329   .2544881     3.58   0.000     .4124454     1.41002
         2004  |   .6635822   .2677673     2.48   0.013      .138768    1.188396
         2005  |   .2132622   .2759962     0.77   0.440    -.3276804    .7542048
         2006  |   .2055204   .3177095     0.65   0.518    -.4171788    .8282196
         2007  |   .0070632   .3180742     0.02   0.982    -.6163507    .6304771
         2008  |  -.4258888   .2031861    -2.10   0.036    -.8241263   -.0276514
         2009  |  -.1525135   .2025328    -0.75   0.451    -.5494704    .2444435
         2010  |  -.2249248    .181555    -1.24   0.215     -.580766    .1309164
         2011  |  -.2851735   .1338686    -2.13   0.033    -.5475511   -.0227958
         2012  |    -.54935   .0686513    -8.00   0.000    -.6839041   -.4147959
         2013  |  -.6197236   .0624535    -9.92   0.000    -.7421302    -.497317
         2014  |  -.4995681   .0395978   -12.62   0.000    -.5771784   -.4219578
         2015  |          0  (omitted)
         2016  |          0  (omitted)
         2017  |          0  (omitted)
         2018  |          0  (omitted)
               |
         _cons |  -.7398958   .8294814    -0.89   0.372    -2.365649    .8858579
--------------------------------------------------------------------------------
convergence not achieved
r(430);

[1] https://www.statalist.org/forums/for...binomial-model
[2] https://www.statalist.org/forums/for...sson-estimates
[3] https://www.statalist.org/forums/for...-fixed-effects
[4] https://www.statalist.org/forums/for...ial-regression
[5] https://www.stata.com/statalist/arch.../msg00288.html

[Joao Santos Silva]

Dear Sebastian Witteler,

My first guess was that you may actually have underdispersed data an in that case the estimator does not converge. However, if you have the same issues with FE Poisson, the problem must be different and it may be the case that the estimator does not exist, or it may be the case that your dependent variable has some very large values that create numerical problems. I suggest that try to rescale the dependent variable and also try the ppmlhdfe command.

Best wishes,

Joao